Our goal was to calculate annual indices and population trends for all stations that had at least 10 years of hourly data, but we also calculated annual indices for some stations that started compiling their hourly data when HawkCount.org was launched around 2002, in order to include more sites. However, sites with less than 10 years are considered to have insufficient data to estimate a trend reliably, so graphs for those sites do not show a trend line or an estimated rate of change. At each RPI site, species included in analyses were those detected at least once in at least half of the years available.

Data are presented in two formats, “long-term” which represents the full range of years of hourly data available in HawkCount (see trend graph), and “recent 10-years” representing the trend for the period 2001 to 2010 (displayed on trend map).

Because the analysis is now highly automated and depends on direct access to the data in HawkCount, several key sites that were included in the previous 2008 analysis were not included in this analysis due to incomplete datasets in the HawkCount database. We are in the process of updating these online records and will add the analyses as they become available.

How
to read the population graphs

This
following example provides the long-term
population trend for Osprey as calculated for Hawk Mountain Sanctuary
based on fall migration data, as indicated in the chart title. The
linear trend value shown below the title is based on all years
analyzed for that station (e.g. 1966-2010), and is expressed as
annual percent change in population index size. This trend value
assumes a linear and discrete change in population size among years
over the time period examined. The significance level is expressed by
the p value: values of 0.05 or less are generally considered
statistically significant (calculation methods for the trend and p
value are provided below).

The
black dots on the chart are estimated indices of annual population
size as calculated by the statistical model. They
are expressed on a linear scale and represent the average of the
predicted number of individual birds detected per hour of survey. If
present, the blue line represents the linear trend.

Trend
maps

Trend
maps combine the calculations from all RPI stations
to easily visualize the overall population trend of a species over a
large area. Having several stations with the same population trend
strongly re-enforces our confidence that the results we see are
representative of the underlying population trends. To ensure that
all trends are directly comparable, we only used the trend based on
the most recent 10 years for each station, and only for stations with
adequate coverage during that period. The example below represents
the population trends of Bald Eagle based on fall migration data in
eastern North America. Green arrows going up represent all cases
where the 10-year population trend is significantly positive, red
arrows going down represent significant population declines and blue
dots represent non-significant changes. Blue arrows (up or down)
represent near-significant trends (p value between 0.05 and 0.10).
Note that the size of the green and red arrows is also proportional
to the magnitude of the increase of decline, as explained in the map
legend. You can click on any of the markers to see more details about
the station name, the trend and period covered, as well as the
significance level. You can also zoom in or out to better see the
details in areas where there are several nearby stations, such as
along the Appalachian Mountains.

Analysis
methods

Annual population indices and long-term population trends were
estimated using Generalized Additive Models with Poisson distribution
and log link (mgcv package, R-Project 2010). Additive Models were first described in the 1980’s (e.g., see
Hastie and Tibshirani 1986), and are an extension of Generalized
Linear Models, first described in the early 1970s (e.g., see Nelder
and Wedderburn 1972).

Annual
indices of population size were calculated as the mean of predicted
hourly counts each year based on the following regression:

g(E(Yijk))
= αk
+ ƒ1(X1ijk)+
ƒ2(X2ijk)
,
(eq. 1)

where
g() indicates a log-link between the mean of Yijk
and the predictor function for the Poisson model; Yijk
= hourly observation count (number of hawks per hour) in hour i, on
day j, in year k; αk
is the intercept (year factor) for year k; X1ijk
= day of year (Julian date); X2ijk
=, hour of the day; f1
and f2
are smoothing functions for day of the year and hour of the day,
respectively. Cases were weighted by W = the ratio of observation
length (typically one hour, but sometimes less than one hour) to
total number of observation hours each year.

A
trend in population index was estimated using the same model
structure, but with year as a continuous variable X0
to replace the αk
factors:

g(E(Yijk))
= β*X0ijk
+ ƒ1(X1ijk)+
ƒ2(X2ijk)
,
(eq. 2)

The
trend was calculated as the % rate of change per year = 100*(exp(β
)-1). This converts the year coefficient, which is an estimate of
the instantaneous rate of change per year, to an estimate of the
discrete rate of change per year between any year and the next
following year.

Because
the p-value for the year coefficient is overly-optimistic using
generalized linear and additive models (degrees of freedom are based
on the number of observations as opposed to the number of years,
incorrectly resulting in highly significant effects), we used an
alternative method based on Monte Carlo simulation to estimate a
p-value for the trend. To do so, each dataset was re-analyzed 1000
times, with the year term randomized each time without replacement.
This tested how many times out of 1000 a trend larger than the year
coefficient from eq.2 was achieved, essentially providing a
probability that the trend was significantly different from zero.

J.A. Nelder and R.W.M. Wedderburn. 1972.
Generalized Linear Models. Journal of the Royal Statistical Society,
Series A (General). 135(3): 370-384.

Availability
of data

All
graphs and maps are available from BSC’s NatureCounts web site:
http://www.naturecounts.ca/rpi/,
as well as from http://hawkcount.org.
RPI stations with a bit of technical skills can easily copy a small
line of script and embed the population trends into their own web
site if they wish. To do so, simply define the population trends that
you would like to see on NatureCounts and look for the link that says
“To insert the graphs below in your own web site using our web
service click here.”

Annual
indices and trends can also be downloaded from NatureCounts in an
Excel compatible format, if you wish to create your own graphs for
presentation. Simply look for the Download button of the population
trend tool on NatureCounts.